Delta to Star Conversion
In this chapter, let us discuss about the Delta to Star Conversion.
Delta Network
Consider the following delta network as shown in the following figure.
The following equations represent the equivalent resistance between two terminals of delta network, when the third terminal is kept open.
Star Network
The following figure shows the equivalent star network corresponding to the above delta network.
The following equations represent the equivalent resistance between two terminals of star network, when the third terminal is kept open.
Star Network Resistances in terms of Delta Network Resistances
We will get the following equations by equating the right-hand side terms of the above equations for which the left-hand side terms are same.
Equation i
Equation ii
Equation iii
By adding the above three equations, we will get
Equation iv
Subtract Equation ii from Equation iv.
By subtracting Equation iii from Equation iv, we will get
By subtracting Equation 1 from Equation 4, we will get
By using the above relations, we can find the resistances of star network from the resistances of delta network. In this way, we can convert a delta network into a star network.
Example :
Let us calculate the resistances of star network, which are equivalent to that of delta network as shown in the following figure.
Given the resistances of delta network as R1 = 10 Ω, R2 = 60 Ω and R3 = 30 Ω.
We know the following relations of the resistances of star network in terms of resistances of delta network.
Substitute the values of R1, R2 and R3 in the above equations.
So, we got the resistances of star network as RA = 6 Ω, RB = 18 Ω and RC = 3 Ω, which are equivalent to the resistances of the given delta network.
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